WPP #7

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Student Problem #4

This is a graph of a logarithmic function where the function, its key points, its (horizontal) asymptote, its x-intercept, its y-intercept, its domain, and its range is shown. Pay special attention to the range, it is infinite both ways which is the exact opposite of exponential functions where their domain is infinite both ways.

Student Problem #3

This is a graph of an exponential function where the function, its key points, its asymptote, its x-intercept, it y-intercept, its domain and its range is shown. Pay close attention to the function and be aware that h is the opposite of what it is because even though it says "x-2", h is actually positive 2. Also be aware of the fact that there is no x-intercept because 1) you get an undefined answer when solving for it and 2) the graph will not hit the x-axis because the vertical asymptote will not allow it.

Student Problem #6

This is an example of a partial fraction decomposition with repeated factors. You do the exact same thing as the PFD with distinct factors except that when you start, the factors that are repeated will be separated into separate fractions. You count up the powers and include the factors as many times as the exponent number.

Student Problem #5

This is picture shows my example of solving a partial fraction decomposition with distinct factors. To solve a partial fraction decomposition with distinct factors problem, first you have to factor the denominator if possible or if not already done (x * x+1 * x-1). Then for each factor, use a letter beginning with A as your numerator and the factor as your denominator (A/x, B/x+1, C/x-1). Next, you have to add these new fractions with each other (A/x + B/x+1 + C/x-1) and set it equal to the original fraction. Now you would need the same denominator to go any further so multiply each fraction with whats missing and you will get like terms. Simplify these like terms and turn it into a system. Solve the system and the substitute the answers with the letters of the fraction.